This article isn't about your typical solid-body electric guitar clean sound. That kind of sound typically has a bit of something extra to round out the tone of a base sound that's mostly a string's vibration in the magnetic field of a pickup. Rather, this article is about the kind of clean amplification that you'd use on an acoustic or jazz guitar.
There are many amplifiers suitable for this application. These amplifiers are marketed mostly as acoustic-guitar amplifiers or jazz-guitar amplifiers, although in practice the applications are interchangeable. Keyboard amps also fall into this niche. All of these amps share the characteristics of having a nominally flat frequency response and very low distortion.
However, if you're after clean reproduction of your guitar then most PAs (excluding the little portable plastic ones) will always offer better reproduction than a stage amp.
Most of the places I play have their own PA. A few of these installations are in very small rooms and consist of a couple of good powered speakers fed by a mixer. Most of the Portland live-music venues that have a capacity of 50 or more people have a permanent PA installation with a pro-quality board, multiple power amps, multiple main speakers and multiple stage monitors.
After several years I finally realized that carrying an amp - even a very small and lightweight amp - is wasted effort. With my own amp I can hear my guitar exactly the way I want. Unfortunately, what I hear from my amp is not what goes to the main speakers. In quite a few cases I have been unpleasantly surprised by the sound that comes back at me from room reflections when I turn down my stage amp.
I've learned to rely on hearing myself through stage monitors or - in the case of the very small venues - via the sound in the room from the main speakers. I know that when I adjust the sound of my instrument to sound good to me, the audience will hear the same sound that I hear.
At home I play through ... believe it or not ... a good PA, knowing that in a different room, playing through someone else's PA, the sound will be very close to my expectations.
I still have my AER Compact 60 for the rare occasions when I'm invited to play in a very small space that doesn't have its own PA. That situation is extremely rare around here, confined mostly to art galleries and smaller restaurants.
As far as connecting the guitar to a PA, you can use either a DI box or a multi-FX processor.
The DI box is the simplest and will appeal to analog purists. Be certain to use an active DI in order to present the proper load impedance to the guitar. A passive DI will alter both the sound of the pickups and the response of the guitar's tone and volume controls.
Examples of active DIs include the Behringer DI-1000 at about US$40 and the Countryman Type 85 at about US$165. Most people won't hear any substantive difference in sound quality between the two. I bought the Countryman because I know it'll last forever.
If you're accustomed to adding effects to your sound, you can either have the sound tech patch in a processor at the board or run pedals between your guitar and the DI. I've done it both ways. Using your own pedals gives you the benefit of familiarity at the expense of more to carry and set up. Patching in studio-quality effects at the board gives you higher quality (the differences can be significant) at the risk of not getting exactly the sound to which you've become accustomed.
A multi-FX processor offers the benefit of an all-in-one solution combining a proper guitar input circuit, multiple effects, a modeled amplifier and (sometimes) a built-in DI. I use a Digitech RP355 (US$200) that offers all of the above features plus a simple looper. The RP355 with its power supply, an assortment of cables, and the carrying bag weighs in at about six pounds. Although the Digitech RPs are unusually easy to program, I normally play through one of the RP355's stock patches for a clean Fender Twin sound with a nice hall reverb, a bit of echo and some stereo chorus, plus a (modeled) Tubescreamer for leads in the more "rocking" tunes.
I have been exclusively using digital modeling for nearly three years after having been a "tube snob" for many years. The Digitech RP (first the 350, then the 355) has been my "go to" processor for more than half that time. Anyone who still believes that modeling somehow "sounds digital" really should check out one of the newer Digitech products. (If you have deep pockets, the ten-times more expensive Fractal Axe-FX will appeal to you, even if the difference in clean guitar sounds is hardly noticeable.)